Is it possible to split a .blend file?
First, a workflow question about your scene: might it work just as well to set up a different scene in the same blend file, dividing the groups between the two scenes?

If not, I think the fastest way within blender would be to save your blender file under a new name (or twice, each under it's own new name) and delete the objects in the group you want to split out in one copy, and delete all of the other objects in the other copy. (Keeping the original unchanged is just part of my standard workflow. I'm too afraid of deleting an object from both copies and losing it. Your mileage may vary.)